510.BJBJR0010.1302/2046-3758.510.BJR-2016-0078.R1
research-article2016
Freely available online open
BJR
L. Ernstbrunner,
J-D. Werthel,
T. Hatta,
A. R. Thoreson,
H. Resch,
K-N. An,
P. Moroder
Mayo Clinic,
Rochester, Minnesota,
United States
„„L. Ernstbrunner, MD,
Orthopaedic Surgeon,
Department of Orthopaedics and
Traumatology, Paracelsus Medical
University, Salzburg, Austria and
Department of Orthopaedics,
Balgrist University Hospital,
University of Zurich, Switzerland,
Zurich, Switzerland.
„„J-D. Werthel, MD, Orthopaedic
Surgeon, Department of
Orthopedic Surgery,
„„T. Hatta, MD, Orthopaedic
Surgeon, Department of
Orthopedic Surgery,
„„A. R. Thoreson, ME, Medical
Engineer, Department of
Orthopedic Surgery,
„„K-N. An, PhD, Professor
Emeritus, Department of
Orthopedic Surgery, Mayo Clinic,
200 First Street SW, Rochester, MN
55905, USA.
„„H. Resch, MD, Orthopaedic
Surgeon, Department of
Orthopaedics and Traumatology,
Paracelsus Medical University,
Salzburg, Austria.
„„P. Moroder, MD, Orthopaedic
Surgeon, Department of
Orthopaedics and Traumatology,
Paracelsus Medical University,
Salzburg, Austria and Center for
Musculoskeletal Surgery, Charite
Universitaetsmedizin, Berlin,
Germany.
Correspondence should be sent to
Mr L. Ernstbrunner;
email: lukas.ernstbrunner@stud.
pmu.ac.at
doi: 10.1302/2046-3758.510.BJR2016-0078.R1
Bone Joint Res 2016;5:453–460.
Received: 17 Mar 2016
Accepted: 29 June 2016
vol. 5, NO. 10, October 2016
Access
„„ Shoulder and elbow
Biomechanical analysis of the effect of
congruence, depth and radius on the
stability ratio of a simplistic ‘ball-andsocket’ joint model
Objectives
The bony shoulder stability ratio (BSSR) allows for quantification of the bony stabilisers
in vivo. We aimed to biomechanically validate the BSSR, determine whether joint incongruence affects the stability ratio (SR) of a shoulder model, and determine the correct parameters (glenoid concavity versus humeral head radius) for calculation of the BSSR in vivo.
Methods
Four polyethylene balls (radii: 19.1 mm to 38.1 mm) were used to mould four fitting sockets in
four different depths (3.2 mm to 19.1mm). The SR was measured in biomechanical congruent
and incongruent experimental series. The experimental SR of a congruent system was compared with the calculated SR based on the BSSR approach. Differences in SR between congruent and incongruent experimental conditions were quantified. Finally, the experimental SR
was compared with either calculated SR based on the socket concavity or plastic ball radius.
Results
The experimental SR is comparable with the calculated SR (mean difference 10%, sd 8%;
relative values). The experimental incongruence study observed almost no differences (2%,
sd 2%). The calculated SR on the basis of the socket concavity radius is superior in predicting
the experimental SR (mean difference 10%, sd 9%) compared with the calculated SR based
on the plastic ball radius (mean difference 42%, sd 55%).
Conclusion
The present biomechanical investigation confirmed the validity of the BSSR. Incongruence
has no significant effect on the SR of a shoulder model. In the event of an incongruent system,
the calculation of the BSSR on the basis of the glenoid concavity radius is recommended.
Cite this article: Bone Joint Res 2016;5:453–460.
Keywords: Shoulder instability; Stability ratio; Bony shoulder stability ratio
Article focus
„„ Is the bony shoulder stability ratio (BSSR)
valid?
„„ Does incongruence affect the stability
ratio (SR) of a shoulder model?
„„ Is it valid to use the radius of the glenoid
concavity of an incongruent shoulder
joint in order to calculate the BSSR
in vivo?
Key messages
„„ The BSSR was proved valid for congruent
and incongruent systems.
„„ For the calculation of the BSSR in vivo, the
use of the radius of the glenoid concavity
is recommended over the use of the
humeral head radius.
„„ Our study findings support the use of the
BSSR for in vivo CT-based determination
of bony shoulder stability.
Strengths and limitations
„„ First biomechanical study analysing the
effect of joint incongruence on the SR.
„„ This study determines the correct parameters (glenoid concavity radius versus
humeral head radius) for calculation of
the BSSR in vivo.
„„ Material properties and friction coefficients are limitations of the present study.
453
454
Introduction
L. Ernstbrunner, J-D. Werthel, T. Hatta, A. R. Thoreson, H. Resch, K-N. An, P. Moroder
In shoulder instability research, the ratio of the peak
translational force causing dislocation to the compressive
load that provides stability is called the stability ratio
(SR).1,2 The ratio is determined by the morphology of the
articulating surfaces,1,3 and in clinical practice largely
depends on the integrity and geometry of the glenoid. It
is known that patients with a glenoid defect are at high
risk of recurrent instability,4,5 which necessitates glenoid
reconstruction surgery by means of coracoid transfers,
iliac crest bone graft transfers, or allografting.6-11 On the
other side, atraumatic and traumatic shoulder instability,
without any sign of glenoid bone loss, is associated with
an inherent flattening of the bony glenoid concavity.12
Thus far, glenohumeral stability in experimental studies has been described either by the SR1,3,5,13 or by displacement after applying a predetermined translational
force.14-18 Oosterom et al19 aimed to predict stability by
means of the “translational stiffness” of the shoulder after
joint replacement. Based on their mathematical model
for circular shapes, translational force over the “distance
to dislocation” can be calculated. Most recently, Willemot
et al20 derived a mathematical model based on machine
design principles. The humeral head as a follower translates over the cam-like glenoid surface, an applicable
concept for non-circular shapes like the native glenohumeral anatomy. However, none of the reported studies described a method allowing for calculation of
glenohumeral stability in daily clinical practice.
Lazarus et al1 aimed to approximate the SR based on
mathematical considerations. The relationship between
the effective glenoid concavity depth and the SR was
described by an empirical equation. This equation was
based on a linear relationship between the two factors.
Moroder et al12 have presented a theoretical model to calculate the bony shoulder stability ratio (BSSR). In this
CT-based study, the BSSR was calculated based on the
patients’ glenoid morphology, allowing for quantification of the passive bony stabilisers of a human shoulder.
It was shown that the relationship between the glenoid
concavity depth and the SR is non-linear.
The BSSR is based on a theoretical congruent joint, the
humeral head and the glenoid concavity having the same
radius of curvature. Calculations of the BSSR in vivo were
therefore conducted with both glenoid and humeral
head radii.12 However, several studies have shown that
the bony structures of the glenohumeral joint are incongruent, with the glenoid concavity having a larger radius
than the humeral head.21-24 Yet it is not clear which of the
radii can be used for valid in vivo calculations of the bony
shoulder stability.
The first aim of the present study was to validate the
BSSR with a biomechanically relevant model. Secondly,
we aimed to analyse the effect of joint incongruence on a
shoulder model and subsequently on a mathematical
equation based on a theoretical congruent joint. Finally,
we aimed to analyse which of the radii, glenoid concavity
or humeral head, should be used for valid calculations of
the BSSR in vivo. We hypothesised that the congruent
experimental SR would not be significantly different from
the calculated SR based on the BSSR approach, that
incongruence has no effect on the SR of a simplistic balland-socket joint, and that the radius of the glenoid concavity, rather than of the humeral head, should be used
for calculation of the BSSR in vivo.
Materials and Methods
Model preparation. A total of four high density polyethylene (HDPE) plastic balls with four different radii of
curvature were used in the present study. Based on morphological analyses,21,25 radii were selected to be 19.1
mm (Ba), 25.4 mm (Bb), 31.8 mm (Bc) and 38.1 mm (Bd).
Plastic balls were mounted on an aluminium rod, forming
an analogue to a human proximal humerus. Similar plastic balls were used as a pattern to mould four fitting sockets from resin (Smooth-Cast 65D, Smooth-On, Macungie,
Pennsylvania) with matching radius of curvature (Sa, Sb,
Sc, Sd). Furthermore, each socket was moulded in four different concavity depths: 3.2 mm (I), 6.4 mm (II), 12.7 mm
(III) and 19.1 mm (IV). In total, 16 different sockets were
created for the experiment. In order to minimise friction,
the surfaces of all moulded sockets were smoothed with
240-grit sandpaper.
Testing apparatus. Components were evaluated using
a custom multi-axis electromechanical testing machine
described in previous studies of shoulder stability.13,26
Briefly, the system consists of a six-axis load cell (model
45E15A-E24ES-A; JR3, Inc., Woodland, California) fitted on
a motorised XY table (DCI Design Components, Franklin,
Massachusetts), the movement of which simulates anterior-posterior or superior-inferior motion. Sockets were
mounted to the XY table (Fig. 1). The z-axis is pneumatically controlled and compressive (medial-lateral) load
is applied to the humerus analogue with motion measured with a linear potentiometer (TR-50; Novotechnik,
Stuttgart, Germany). According to the manufacturer, the
capacity and resolution of the load cell are 100 N and
1.3 N, respectively (Fig. 1). Following previous studies,
measuring the point where the ball was seated at the
deepest part of the socket concavity identified the neutral position.13,26 A 50-N concavity compression force,
selected based on previous studies,1,13,27 was applied to
the plastic ball by the pneumatic cylinder. All analyses
were based on a normalised displacement, where each
head size was displaced one diametrical distance anteriorly at 2 mm/s. The translational force was defined as the
maximum force observed as the ball translated across its
normalised distance.
Test conditions. Each experiment and condition was
repeated three times to evaluate repeatability of the results.
BONE & JOINT RESEARCH
Biomechanical analysis of the effect of congruence
Fig. 1
A photograph of the custom testing machine and the experimental setup.
The high density polyethylene plastic ball is mounted on an aluminium rod,
whereas the moulded socket is mounted on an aluminium plate attached to
the load cell (blue).
455
The peak translational force was measured in two different ways: with congruent radii of curvature between
the ball and socket (Fig. 2a) and with a series of incongruent radii of curvature between the ball and socket (Fig. 2b).
In the validation series, each ball (Ba to Bd) was translated against a mating socket (Sa to Sd) of each of the different concavity depths (I to IV) (Table I). The ratio of the
peak translational force causing dislocation and the constant concavity compression force was defined as the SR
for each condition.1,3
The second testing series evaluated incongruent radii
of curvature. As previously reported, mismatch was
defined as the ratio of the ball radius to the radius of curvature of the socket.19,21 Our mismatched conditions had
a ratio of 0.75, 0.80 and 0.83. In other words, we articulated the 19.1 mm ball (Ba) with the 25.4 mm socket (Sb)
(ratio = 0.75), the 25.4 mm ball (Bb) with the 31.8 mm
socket (Sc) (ratio = 0.80) and the 31.8 mm ball (Bc) with
the 38.1 mm socket (Sd) (ratio = 0.83). Each ball was
translated against the incongruent sockets of four different depths (I to IV) (Table I).
Statistical analysis. The BSSR (i.e. calculated SR) for
each ball-and-socket configuration was calculated as
described by Moroder et al.12 The ratio between translational force (T) and compressive force (C) (Equation 1)
was expressed in terms of the radius of curvature (r) and
concavity depth (d) based on Pythagorean trigonometric
identities (Equation 2). The full derivation of Equations
1 and 2 are given in the supplementary material.
Radius of curvature
of sockets (Sa to Sd)
Concavity depths (I to IV)
Fig. 2a
Radius of curvature
of balls (Ba to Bd)
Fig. 2b
The radii of curvature of the ball (Ba to Bd) and socket (Sa to Sd), and its concavity depths (I to IV) are shown; a) the radius of the socket (dashed arrow) is the circumference, depicted by the socket and the dashed circle arc, starting from the socket’s rim. The radius of the ball matches the circumference; b) in an incongruent system, the radius of the ball (continuous arrow and circumference) does not match the socket’s circumference depicted by the socket and dashed circle arc.
vol. 5, No. 10, October 2016
456
L. Ernstbrunner, J-D. Werthel, T. Hatta, A. R. Thoreson, H. Resch, K-N. An, P. Moroder
Table I. All applied testing conditions
Test conditions
Congruent System
Ba : Sa (I)
Ba : Sa (II)
Ba : Sa (III)
Ba : Sa (IV)
Incongruent System
.75
Ba : Sb (I)
Ba : Sb (II)
Ba : Sb (III)
Ba : Sb (IV)
Bb : Sb (I)
Bb : Sb (II)
Bb : Sb (III)
Bb : Sb (IV)
Bc : Sc (I)
Bc : Sc (II)
Bc : Sc (III)
Bc : Sc (IV)
.80
Bb : Sc (I)
Bb : Sc (II)
Bb : Sc (III)
Bb : Sc (IV)
Bd : Sd (I)
Bd : Sd (II)
Bd : Sd (III)
Bd : Sd (IV)
.83
Bc : Sd (I)
Bc : Sd (II)
Bc : Sd (III)
Bc : Sd (IV)
0.75, 0.80 and 0.83 indicate the ratio of the mismatched radii
Ba to Bd, radii of curvature of the balls; Sa to Sd, radii of curvature of the sockets; I to IV, concavity depths of the sockets
BSSR =
T
C
(Equation 1)
2
r −d 
1− 

 r 
BSSR =
r −d
r
(Equation 2)
BSSRs calculated from this approach were validated
against SRs derived from experimental data of a congruent
system. To analyse the influence of incongruence, experiment-derived SRs of congruent conditions were compared
with their incongruent counterparts. In order to determine
the correct parameters (glenoid concavity radius versus
humeral head radius) for calculation of the BSSR in vivo,
the experimental SR was compared with the calculated SR
based on the socket concavity or plastic ball radius.
In the validation study, data were analysed by comparing SRs with the same radii of curvature of the ball and
socket but different depths (e.g. experimental Ba : Sa (I to
IV) versus calculated Ba : Sa (I to IV)) and with same depth
but different radii of curvature (e.g. experimental Ba-d : Sa-d
(I) versus calculated Ba-d : Sa-d (I)).
In order to prove the influence of incongruence on the
SR of a simplistic ball-and-socket joint, data were analysed
by comparing only experimental SRs with the same radii of
curvature (same mismatched radii) of the ball and socket,
but different depths (e.g. 0.75 mismatch; Bb : Sb (I to IV)
versus Ba : Sb (I to IV)).
Finally, the experimental SR was compared with the
calculated SR based on the radius of the socket concavity
and the calculated SR based on the radius of the plastic
ball. Data were analysed by comparing the experimental
SRs with each of the corresponding calculated SR based
on the socket concavity or plastic ball radius (e.g. experimental Ba : Sb (I to IV) versus calculated Sb (I to IV); experimental Ba : Sb (I to IV) versus calculated Ba (I to IV)).
Paired sample t-tests or Wilcoxon signed-rank tests
were applied using SPSS Statistics (Version 22, IBM
Corporation, Chicago, Illinois). In addition, differences
between experimental versus calculated SR and congruent versus incongruent SR were plotted on a graph. In
order to evaluate repeatability of the results, test-retest
reliability was proved. A p-value less than 0.05 indicated
statistical significance.
Results
Experimental versus calculated SR. In the test condition Ba
(IV) :): Sa (IV), the measured translational force exceeded
the load cell capacity. These results were excluded.
The mean difference in this series was 10% (sd 8%)
(relative value) (Fig. 3). Comparing the SRs of the simplistic ball-and-socket joints, no significant differences were
observed, except in the comparisons Bb : Sb (I to IV)
(p = 0.010;) and Bd : Sd (I to IV) (p = 0.049), as well as in
Ba-d : Sa-d (I) (p = 0.029) and Ba-d : Sa-d (III) (p = 0.026). Of
these significant comparisons, the mean difference in Bb :
Sb (I to IV) was 11% (sd 5%) and in Bd : Sd (I to IV) 3%
(sd 3%) (relative value). On the other side, the mean difference in Ba-d : Sa-d (I) was 8% (sd 5%) and in Ba-d : Sa-d (III)
12% (sd 8%) (relative value).
The test-retest reliability of the congruent experimental SRs was proved excellent (R = 0.995).
Congruent versus incongruent SR. In this experimental
study, the mean difference was 2% (sd 2%) (relative
value) (Fig. 4). SRs of congruent compared with incongruent simplistic joints revealed no significant differences,
except for the comparison Bd : Sd (I to IV) versus Bc : Sd
(I to IV) (0.83 mismatch). In this significant comparison,
the mean difference gave a result of 1% (sd 1%) (relative
value).
Repeatability of the incongruent experimental SRs
observed an excellent test-retest reliability (R = 0.995).
Experimental versus calculated SR based on socket concavity radius and experimental versus calculated SR based on
plastic ball radius. Comparing the experimental SR of an
incongruent system with the corresponding calculated
SR based on the radius of the socket concavity, a mean
difference of 10% (sd 9%) (relative value) was observed.
When comparing the experimental SR with the corresponding calculated SR based on the radius of the plastic
ball, a mean difference of 42% (sd 55%) (relative value)
was proved.
Discussion
The biomechanical relationship between the SR and the
glenoid concavity was explained in previous studies.1,3,13,28
Lippitt et al3 showed that the greater the glenoid concavity, the greater the SR. Yamamoto et al5,28 observed that
loss of glenoid concavity due to glenoid bone loss results
in a significant decrease of SR of the shoulder,5 which cannot be overcome by mere capsulolabral repair but necessitates glenoid reconstruction surgery.28 The measurement
of the SR is, however, only possible by means of in vitro
biomechanical testing. Until recently, there was no
BONE & JOINT RESEARCH
Biomechanical analysis of the effect of congruence
457
4.00
3.50
Stability ratio
3.00
Calculated SR (Ba : Sa; I to III)
Congruent experimental SR (Ba : Sa; I to III)
Calculated SR (Bb : Sb; I to IV)
Congruent experimental SR (Bb : Sb; I to IV)
Calculated SR (Bc : Sc; I to IV)
Congruent experimental SR (Bc : Sc; I to IV)
Calculated SR (Bd : Sd; I to IV)
Congruent experimental SR (Bd : Sd; I to IV)
2.50
2.00
1.50
1.00
0.50
0.00
0.0
5.0
10.0
15.0
Socket depth (mm)
20.0
25.0
Fig. 3
Graph illustrating the difference between the mean experimental and calculated stability ratio (SR) for different radii of curvature of the ball-and-socket configuration in a congruent system. Ba : Sa to Bd : Sd = radii of curvature of the congruent balls and sockets; I to IV = concavity depths of the sockets.
4.00
3.50
Stability ratio
3.00
2.50
Incongruent experimental SR (Ba : Sb; I to IV)
Congruent experimental SR (Bb : Sb; I to IV)
Incongruent experimental SR (Bb : Sc; I to IV)
Congruent experimental SR (Bc : Sc; I to IV)
Incongruent experimental SR (Bc : Sd; I to IV)
Congruent experimental SR (Bd : Sd; I to IV)
2.00
1.50
1.00
0.50
0.00
0.0
5.0
10.0
15.0
Socket depth (mm)
20.0
25.0
Fig. 4
Graph comparing the effect of experimental radii incongruence to experimental radii congruence regarding the resulting stability ratio (SR). Bb : Sb to Bd : Sd =
radii of curvature of the congruent balls and sockets; Ba : Sb to Bc : Sd = radii of curvature of the incongruent balls and sockets; I to IV = concavity depths of the
sockets.
technique available to estimate the SR of a glenohumeral
joint in vivo. Moroder et al12 presented a CT-based technique, which allows for prediction of the SR of the glenohumeral joint. It was named the bony shoulder stability
ratio (BSSR) since it only takes into consideration the bony
glenoid morphology visible on CT scans and neglects the
stability-contributing effects of soft-tissue structures. The
BSSR represents an easy method to calculate the stability
ratio created by the bony glenoid concavity and thus offers
vol. 5, No. 10, October 2016
the possibility to calculate the actual biomechanical effect
of glenoid concavity alterations or glenoid reconstruction
surgery in vivo. However, in the reported study it could not
be clarified whether the mathematical equation based on a
theoretical congruent joint is also valid for in vivo measurements on an incongruent glenohumeral joint with mismatching radii of curvature.
In the present study we aimed to biomechanically validate the BSSR by comparing the experimental SR of a
458
L. Ernstbrunner, J-D. Werthel, T. Hatta, A. R. Thoreson, H. Resch, K-N. An, P. Moroder
congruent system with the calculated SR based on the
BSSR approach. According to our results, almost all experimental setups yielded the same results as calculated with
the theoretical model. The mean relative difference in this
series was 10%. The comparisons with statistically significant differences showed mean relative differences of not
more than 12%. Although acceptably small, the presence
of differences between the experimental and calculated
SRs is evident. Willemot et al20 observed in his cam-follower study on mid-range instability a similar tendency,
whereas experimental SRs were constantly smaller than
the calculated SRs and relied on elasticity and friction in
the experimental model. The validity of the BSSR has previously been confirmed by Finite Element Analysis,12
which revealed only negligible discrepancies between the
computer simulation and the BSSR. Accordingly, our
results also prove the validity of the BSSR.
The observed experimental SRs were consistently
slightly smaller than the calculated SRs. According to
Moroder et al,12 increasing the radius of curvature is indirectly related to the SR. We assume that due to the constant concavity load, local deformation of the material
occurs, leading to an increased local radius of curvature
of the socket and resulting in a smaller experimental SR
compared with the calculated SR.
Previous studies described the bony morphology of
the glenohumeral joint as a “golf ball on a tee” phenomenon.12,29 A completely flat “tee” would result in a theoretical BSSR of 0%.12 On the other side, increasing the
concavity depth results in a steep increase of the BSSR.
Increasing the concavity depth up to its radius of curvature, the BSSR would increase exponentially and the ball
would be secured against any translational force. It was
described as “placing the golf ball in an egg cup”.12 The
same finding was observed in this study. A radius of curvature of the ball of 19.1 mm (Ba IV) and a concavity
depth of 19.1 mm (Sa IV) led to translational forces
exceeding the load cell capacity, and these results had to
be excluded.
The BSSR is based on a congruent articulating system
with the same radii of curvature for both the glenoid
concavity and the humeral head.12 However, it is known
that the cartilage of the humeral head and the glenoid
are better conforming than the underlying bone, which
feature a mismatch regarding their radii.21 According to
our study analysing the effect of incongruence on a
shoulder model, with a mismatch of 0.75 and 0.80, no
significant differences between the congruent and
incongruent experimental SRs could be noted. Only one
experimental setup resulted in a significant difference
between the congruent and incongruent experimental
system, however, the mean relative difference was 1%
(Fig. 4), and almost negligible. Although Hopkins et al30
observed that congruence in anatomic total shoulder
arthroplasty is linearly related to humeral head translations, they also concluded that the force ratio (i.e. the
SR) required to destabilise the shoulder joint is not
affected by congruence. Furthermore, Karduna et al31
described similar patterns of humeral head translation
in native and reconstructed shoulder joints. These findings support our second conclusion, that incongruence
has no effect on the SR of a simplistic ball-and-socket
joint.
The BSSR was calculated using not only the radius of
the glenoid concavity, but also the humeral head
radius.12 A constantly increased BSSR of 10% was
observed. It remained unclear which of the radii can be
used for valid in vivo calculations of the bony shoulder
stability. It was postulated that calculating the BSSR
using the glenoid concavity radius is key in order to estimate the bony shoulder stability based on the mathematical equation for congruent radii. In the present
study, comparing the experimental SR of an incongruent
system with the corresponding calculated SR based on
the radius of the socket concavity observed a mean relative difference of 10%. In comparison, using the radius of
the plastic ball for the corresponding calculated SR, the
mean relative difference was over 40%. Our results conform to recently published studies describing that, independently of the humeral head radius, the glenoid
concavity depth and radius are the determining variables
of the SR.12,19 Oosterom et al19 showed that in shoulder
joint arthroplasty, the radius of curvature of the glenoid
cavity is, besides the concavity depth, the SR-determining
factor. It was observed that varying the humeral head
radii results in similar maximum allowable subluxation
forces, which are only dependent on the radius of the
glenoid concavity.
According to our results, as long as the humeral head
radius is no bigger than the radius of the glenoid concavity, calculating the BSSR in vivo based on the radius of
the glenoid concavity is valid. Although the BSSR relies on
a theoretical congruent glenohumeral joint, the present
study proved that this method is a valid clinical measure
for patients suffering from recurrent glenohumeral instability. Despite this, the mathematical equation is still a
simplified method, and does not consider additional factors such as the glenoid cartilage, the labrum with its
concavity-increasing effect,3 or the negative intra-­articular
pressure.32
Currently, the necessity for bony glenoid reconstruction surgery in patients with anterior shoulder instability
is determined by measuring the lack of glenoid surface
area.13,33-35 Considering glenoid bone loss in its 2D
extent, however, seems to be overly simplistic and might
underestimate the effect of glenoid concavity alterations
on stability. This underestimation might be a possible
explanation for the high long-term failure rate after
BONE & JOINT RESEARCH
Biomechanical analysis of the effect of congruence
soft-tissue-based stabilisation procedures.36-39 The
recently introduced BSSR makes it possible to perform an
in vivo quantification of the stability ratio created by the
glenoid concavity based on CT measurements.12 This
additional information could be useful to determine critical glenoid defects more precisely. Our results prove the
validity of the BSSR formula and provide a reasonable
explanation as to which variable should be used in order
to calculate the patient-specific BSSR in daily clinical
practice.
There are limitations in this study, namely the material
properties and friction coefficients of the ball-and-socket
models. For the validation of the BSSR, a mathematical
equation, this systematic error is negligible. Another limitation is the size effect of the incongruent experimental
setup with increasingly mismatched radii of curvature.
The size of the model could have led to a scaling effect on
the force data, thus influencing the results of the incongruent experimental setup.
In conclusion, biomechanical testing confirmed the
validity of the BSSR. Incongruence has no effect on the SR
of a simplistic ball-and-socket joint. For the calculation of
the BSSR in vivo, the use of the radius of the glenoid concavity is recommended over the use of the humeral head
radius. Finally, our study findings support the use of the
BSSR for in vivo CT-based determination of bony shoulder
stability.
Supplementary material
A description of the relation of the translational (T)
and compressive (C) force vectors to the geometric
parameters radius (r) and concavity depth (d) of the balland-socket configuration can be found alongside this
paper at http://www.bjr.boneandjoint.org.uk/
References
1.Lazarus MD, Sidles JA, Harryman DT II, Matsen FA III. Effect of a chondrallabral defect on glenoid concavity and glenohumeral stability. A cadaveric model.
J Bone Joint Surg [Am] 1996;78-A:94-102.
2.Fukuda K, Chen CM, Cofield RH, Chao EY. Biomechanical analysis of stability and
fixation strength of total shoulder prostheses. Orthopedics 1988;11:141-149.
3.Lippitt SB, Vanderhooft JE, Harris SL, et al. Glenohumeral stability from
concavity-compression: A quantitative analysis. J Shoulder Elbow Surg 1993;2:27-35.
4.Burkhart SS, De Beer JF. Traumatic glenohumeral bone defects and their
relationship to failure of arthroscopic Bankart repairs: significance of the
inverted-pear glenoid and the humeral engaging Hill-Sachs lesion. Arthroscopy
2000;16:677-694.
5.Yamamoto N, Itoi E, Abe H, et al. Effect of an anterior glenoid defect on anterior
shoulder stability: a cadaveric study. Am J Sports Med 2009;37:949-954.
6.Auffarth A, Schauer J, Matis N, et al. The J-bone graft for anatomical glenoid
reconstruction in recurrent posttraumatic anterior shoulder dislocation. Am J Sports
Med 2008;36:638-647.
7.Latarjet M. A propos du traitement des luxations récidivantes de l’épaule. Lyon Chir
1954;49:994-997. (In French)[[bibmisc]]
8.Provencher MT, Ghodadra N, LeClere L, Solomon DJ, Romeo AA. Anatomic
osteochondral glenoid reconstruction for recurrent glenohumeral instability with
glenoid deficiency using a distal tibia allograft. Arthroscopy 2009;25:446-452.
9.Weng PW, Shen HC, Lee HH, Wu SS, Lee CH. Open reconstruction of large bony
glenoid erosion with allogeneic bone graft for recurrent anterior shoulder dislocation.
Am J Sports Med 2009;37:1792-1797.
vol. 5, No. 10, October 2016
459
10.Zhao J, Huangfu X, Yang X, Xie G, Xu C. Arthroscopic glenoid bone grafting with
nonrigid fixation for anterior shoulder instability: 52 patients with 2- to 5-year followup. Am J Sports Med 2014;42:831-839.
11.Petrera M, Veillette CJ, Taylor DW, Park SS, Theodoropoulos JS. Use of fresh
osteochondral glenoid allograft to treat posteroinferior bone loss in chronic posterior
shoulder instability. Am J Orthop (Belle Mead NJ) 2013;42:78-82.
12.Moroder P, Ernstbrunner L, Pomwenger W, et al. Anterior Shoulder Instability Is
Associated With an Underlying Deficiency of the Bony Glenoid Concavity. Arthroscopy
2015;31:1223-1231.
13.Itoi E, Lee SB, Berglund LJ, Berge LL, An KN. The effect of a glenoid defect on
anteroinferior stability of the shoulder after Bankart repair: a cadaveric study. J Bone
Joint Surg [Am] 2000;82-A:35-46.
14.Bryce CD, Davison AC, Okita N, et al. A biomechanical study of posterior
glenoid bone loss and humeral head translation. J Shoulder Elbow Surg
2010;19:994-1002.
15.Elkinson I, Giles JW, Faber KJ, et al. The effect of the remplissage procedure on
shoulder stability and range of motion: an in vitro biomechanical assessment. J Bone
Joint Surg [Am] 2012;94-A:1003-1012.
16.Peltier KE, McGarry MH, Tibone JE, Lee TQ. Effects of combined anterior
and posterior plication of the glenohumeral ligament complex for the repair of
anterior glenohumeral instability: a biomechanical study. J Shoulder Elbow Surg
2012;21:902-909.
17.Schulze-Borges J, Agneskirchner JD, Bobrowitsch E, et al. Biomechanical
comparison of open and arthroscopic Latarjet procedures. Arthroscopy
2013;29:630-637.
18.Sekiya JK, Jolly J, Debski RE. The effect of a Hill-Sachs defect on glenohumeral
translations, in situ capsular forces, and bony contact forces. Am J Sports Med
2012;40:388-394.
19.Oosterom R, Herder JL, van der Helm FC, Swieszkowski W, Bersee
HE. Translational stiffness of the replaced shoulder joint. J Biomech 2003;36:
1897-1907.
20.Willemot L, Thoreson A, Ryan Breighner, et al. Mid-range shoulder instability
modeled as a cam-follower mechanism. J Biomech 2015;48:2227-2231.
21. Zumstein V, Kraljevic’ M, Hoechel S, et al. The glenohumeral joint - a mismatching
system? A morphological analysis of the cartilaginous and osseous curvature of the
humeral head and the glenoid cavity. J Orthop Surg Res 2014;9:34.
22.Iannotti JP, Gabriel JP, Schneck SL, Evans BG, Misra S. The normal
glenohumeral relationships. An anatomical study of one hundred and forty shoulders.
J Bone Joint Surg [Am] 1992;74-A:491-500.
23.Soslowsky LJ, Flatow EL, Bigliani LU, Mow VC. Articular geometry of the
glenohumeral joint. Clin Orthop Relat Res 1992;285:181-190.
24. Walch G, Edwards TB, Boulahia A, et al. The influence of glenohumeral prosthetic
mismatch on glenoid radiolucent lines: results of a multicenter study. J Bone Joint
Surg [Am] 2002;84-A:2186-2191.
25.Walch G, Mesiha M, Boileau P, et al. Three-dimensional assessment of the
dimensions of the osteoarthritic glenoid. Bone Joint J 2013;95-B:1377-1382.
26. Tammachote N, Sperling JW, Berglund LJ, et al. The effect of glenoid component
size on the stability of total shoulder arthroplasty. J Shoulder Elbow Surg 2007;16(3
Suppl):S102-106.
27.Lippitt S, Matsen F. Mechanisms of glenohumeral joint stability. Clin Orthop Relat
Res 1993;291:20-28.
2 8.Yamamoto N, Muraki T, Sperling JW, et al. Stabilizing mechanism in bonegrafting of a large glenoid defect. J Bone Joint Surg [Am] 2010;92-A:20592066.
29.O’Brien SJ, Voos JE, Neviaser AS, Drakos MC. Developmental anatomy of
the shoulder and anatomy of the glenohumeral joint. In: Rockwood CA Jr, Matsen
FA III, eds. The Shoulder. Fourth ed. Philadelphia: WB Saunders Company,
1990:1-31.
30.Hopkins AR, Hansen UN, Amis AA, Taylor M, Emery RJ. Glenohumeral
kinematics following total shoulder arthroplasty: a finite element investigation.
J Orthop Res 2007;25:108-115.
31.Karduna AR, Williams GR, Williams JL, Iannotti JP. Glenohumeral joint
translations before and after total shoulder arthroplasty. A study in cadavera. J Bone
Joint Surg [Am] 1997;79-A:1166-1174.
32.Habermeyer P, Schuller U, Wiedemann E. The intra-articular pressure of the
shoulder: an experimental study on the role of the glenoid labrum in stabilizing the
joint. Arthroscopy 1992;8:166-172.
33.Bushnell BD, Creighton RA, Herring MM. Bony instability of the shoulder.
Arthroscopy 2008;24:1061-1073.
460
L. Ernstbrunner, J-D. Werthel, T. Hatta, A. R. Thoreson, H. Resch, K-N. An, P. Moroder
34.Sugaya H, Moriishi J, Dohi M, Kon Y, Tsuchiya A. Glenoid rim morphology
in recurrent anterior glenohumeral instability. J Bone Joint Surg [Am] 2003;85A:878-884.
35.Schrumpf MA, Maak TG, Delos D, et al. The management of anterior
glenohumeral instability with and without bone loss: AAOS exhibit selection. J Bone
Joint Surg [Am] 2014;96:e12.
36.Castagna A, Markopoulos N, Conti M, et al. Arthroscopic bankart suture-anchor
repair: radiological and clinical outcome at minimum 10 years of follow-up. Am J
Sports Med 2010;38:2012-2016.
37.Cheung EV, Sperling JW, Hattrup SJ, Cofield RH. Long-term outcome of anterior
stabilization of the shoulder. J Shoulder Elbow Surg 2008;17:265-270.
38. Fabre T, Abi-Chahla ML, Billaud A, Geneste M, Durandeau A. Long-term results
with Bankart procedure: a 26-year follow-up study of 50 cases. J Shoulder Elbow Surg
2010;19:318-323.
39.Moroder P, Odorizzi M, Pizzinini S, et al. Open Bankart Repair for the Treatment
of Anterior Shoulder Instability without Substantial Osseous Glenoid Defects:
Results After a Minimum Follow-up of Twenty Years. J Bone Joint Surg [Am]
2015;97-A:1398-1405.
Funding Statement
„„ This research received no specific grant from any funding agency in the public,
commercial or not-for-profit sectors.
Author Contribution
„„ L. Ernstbrunner: Study and preparation of the manuscript.
„„ J-D. Werthel: Study and preparation of the manuscript.
„„ T. Hatta: Study and preparation of the manuscript.
„„ A. R. Thoreson: Study and preparation of the manuscript.
„„ H. Resch: Study and preparation of the manuscript.
„„ K-N. An: Study and preparation of the manuscript.
„„ P. Moroder: Study and preparation of the manuscript.
ICMJE conflict of interest
„„ The authors confirm that there are no conflicts of interest associated with this publication. The authors, their immediate family, and any research foundation with
which they are affiliated did not receive any financial payments or other benefits
from any commercial entity related to the subject of this article. There was no outside funding or grants received that assisted in this study.
© 2016 Ernstbrunner et al. This is an open-access article distributed under the
terms of the Creative Commons Attributions licence (CC-BY-NC), which permits unrestricted use, distribution, and reproduction in any medium, but not for commercial
gain, provided the original author and source are credited.
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